I'm having difficulty with the following situation trying to numerically solve an equation (with vpasolve, or something similar) that uses interp1-interpolated data within the solve. Consider:
with implementation:
syms Z;
vpasolve(Z.^4 == ( muL .* interp1(X,GH,Z) - muH .* interp1(X,GL,Z) )./( muL .* interp1(X,FH,Z) ...
- muH .* interp1(X,FL,Z) ), Z);
where 
and 
are constants, so that the μ-values are constant, and F and G are 2D matrices squeezed to 1D. These 1D matrices are known on a grid Z = 5:15. Then, I'm attempting to solve this equation for Z, which presumably has real-numbered values 
as solution. I assumed vpasolve worked iteratively, with an initial guessed query of Z, such that interp1 with (syms Z) is valid to use inside vpasolve. Of course, this doesn't work. Is there any way to work this? I've simplified things for ease of explanation, but suffice it to say that just doing a polynomial fit on F and G instead of using interp1 is not on the table: the data in the F and G grids need to only be interpolated for non-integer values of Z. Here's some data, just to make it easier to run if needed.
muH = 0.178125;
muL = 0.142500;
GL = [0.2684 0.2690 0.2696 0.2704 0.2714 0.2724 0.2734 0.2746 0.2756 0.2768 0.2781];
GH = [0.3258 0.3280 0.3307 0.3342 0.3381 0.3431 0.3474 0.3520 0.3568 0.3618 0.3670];
FL = 1E-6 .* [0.4234 0.4180 0.4100 0.4017 0.3932 0.3840 0.3766 0.3698 0.3628 0.3554 0.3480];
FH = 1E-6 .* [0.4234 0.4180 0.4100 0.4017 0.3932 0.3840 0.3766 0.3698 0.3628 0.3554 0.3480];
